Skip navigation

If you were to go and do a simple internet search for the phrase “artistic representations of Pi” (and I encourage you do so), you’d find a slew of amazing looking pieces that generally depict what looks like random noise. Sure, the noise may be presented elegantly, but the fact still remains, the digits of Pi, when plotted out, just represent an overall lack of pattern.

You, see, people tend to focus on the actual digits. Before I begin talking about an alternative approach, let’s talk about art in general. Upon the wall of my son’s pre-school classroom is a chart which reads: ELEMENTS OF ART. The elements include: Color, Value, Line, Texture, Shape, Form, and Space. This is a nice list that indicates the sort of elements that I tried to bring to the problem of representing Pi in what I believe are three very interesting ways.

There are a couple of other mathematical concepts that relate to art which I relied on heavily for this project. The first is Symmetry. By imposing symmetry onto Pi, it becomes less about the noise. This I did by folding Pi into a circle. Quite apropos, but it’s been done before.

The second thing I did was by studying which numbers do produce wonderful patterns in art. It turns out that this is done by creating what is called a Sequence. Arguably, the most famous sequence is the Fibonacci Sequence. This is created by using the real numbers and adding them together serially:

1, 1, 2, 3, 5, 8, 13 . . .

The Fibonacci Sequence is a marvel of the mathematical world as well as appears throughout the natural world in countless permutations.

Another famous sequence is the Primes. A number that can’t be divided by any number except itself and 1:

2,3,5,7, 11, 13, 17, 19 . . .

There is an entire library of sequences:


What is missing is the sequence created by adding the digits of Pi serially. I’ve searched and searched for the sequence’s name and for any research into exploring its properties, but, apparently, I’m laying claim to it.

The sequence turns out to be:

3, 4, 8, 9, 14, 23, 25, 31, 36 . . .

One thing you’ll notice about such sequences is that they almost always grow as the sequence progresses. It is because of the relationship between the numbers, rather than just the numbers themselves, that make sequences a great tool for an artist and a mathematician to explore.

It should also be noted that I chose a 36 degree circle because of its divisibility and the fact that it limits most of the sequences I wanted to explore to a range of 6 to 11 numbers. A very manageable set that can be used for multiple purposes, as you’ll see. So, with the limit set to 36, the serialized Pi sequence we are going to explore by encoding into three schemas is once again:

3, 4, 8, 9, 14, 23, 25, 31, 36

These nine numbers will be turned into 3D Shapes, Colors, and Sounds.

To understand my approach, it helps to understand how to form a cardioid – a shape within a circle that resembles a heart.

We’ll be using a 36-degree circle, so it helps to understand how these 36 nodes will be counted. For these examples, we’ll always be using the bottom node as our Starting Point (the node in the South direction, or in the 6 o’clock position. Instead of counting the Starting Point as “1”, however, we consider it to be “0”.

Notice that when you count up one side of the circle that the lines grow longer until you reach the number “18”, which is directly opposite node “0”, and then the lines become shorter incrementally again as you count higher. In essence, the numbers 1-17 all have a corollary number 19-35 so that the distance from 0 to 1 is the same in length as 0 to 35. In the same way, 0 to 2 is the same as 0 to 34, etc.

With all this in mind, it will help to view the next two links and learn about the Cardioid.


Cardioid 2

In creating a Cardioid on a 36-degree circle, each step in the process creates just one instance of a particular number that is always of the formula n = n x 2. This pattern creates a mirrored spiral across the even numbers where the lines grow to node 18 and then shrink again as the numbers go higher.

But let us now consider the act of creating a line from every single node of the same number over and over. Take for example the number “9”. When the number “9” is fully mapped around the circle, a smaller circle appears. This circle of the number “9” is actually formed out of the half-way points of every single line.

But also notice that the number “9” corresponds to the number “27”. Before we move on to a method to differentiate such cases of corollary numbers, let’s take a look at what the number sequence of 3, 4, 8, 9, 14, 23, 25, 31, and 36 looks like when plotted in number circles within a 36-degree circle in pencil.

The pencil version looks pretty amazing, but presents a problem with higher numbers that might get confused with or even overlay lower numbers.

To see the issue clearer, let’s keep in mind that the goal is to create an actual 3D version of the circle using thread for the lines. When constructing a 3D version, the thread gets built from the base upwards. In other words, the thread goes on the loom in the reverse order of the numbers. What happens when higher numbers are covered over with thread as the lower numbers get added?

To see the problem clearer, let’s view several sequences in cross-sectional views.

Interestingly enough, from doing this, we see that the Pi Sequence is actually a great sequence to apply to the 36-degree circle. The Prime Sequence turns out to be a bad choice, at least with 36 degrees. The “odd” nature of Prime Sequence causes several numbers to coincide with their corollary, which would hide the higher number and/or artificially reinforce the lower numbers (e.g 5 & 31, 7 & 29, 13 & 23, 17 & 19).

This doesn’t happen with the Cardioid because the even numbers are only “counted” one instance whereas using our method, each number is “counted” 36 times to form the full circle.

An artistic method of differentiating the lower and higher corollaries is to map each number to a color. I chose to use the RBG color wheel because it is already mapped onto a circle. Plus, the values are precisely determined – even though I chose not to seek out thread colors of such exacting values.

By adding color values to the circle we can see quite easily the difference between a “yellow 6-valued circle” and a “magenta 30-valued circle”.

The end result is like looking through a rainbow of the digits of the Pi Sequence.

This next picture illustrates the rainbow color of the cross section which is formed.

Not wanting to stop there, I chose to apply the sequence to music.

The problem then becomes how to project a musical scale onto a 36-degree circle? It just so happens that 36 can be divided into 12 sets of 3 numbers. The Western musical scale also has 12 note values in an octave for the Chromatic Scale.

This process, unlike the previous two of mapping numbers and colors, cannot be reversed, though. Since numbers 1, 2, and 3, could all become the first note, there is no way to know the first note and from that extrapolate backwards whether that note is exactly 1, 2, or 3. But it is still a fun exercise to see how the Pi Sequence sounds when plotted onto the circle of notes.

For my version, I chose to start with the note A and build from A being the root note.

Note               Note Value      Original Number

A                      0                      1-3

A#/Bb              1                      4-6

B                      2                      7-9

C                      3                      10-12

C#/Db              4                      13-15

D                      5                      16-18

D#/Eb              6                      19-21

E                      7                      22-24

F                      8                      25-27

F#/Gb              9                      28-30

G                     10                    31-33

G#/Ab             11                    34-36

A (again 1 octave higher)

Our Pi Sequence (3, 4, 8, 9, 14, 23, 25, 31, 36) becomes:

A, A#, B, B, C#, E, F, G, G#

This creates 9 notes and I chose to write in the unorthodox time signature of 9/8 time. My method was to break down the notes into three groups of three notes each. I also wrote a return to Pi at the end that emphasized the numbers 3, 1, 4, 1, 5, and then 9 but using the 9-note sequence as a reprise. 314159 then plays over and over until fade out.

Plotted on a midi sequencer, it looks like this when played twice. I lowered the last 3 notes an octave.

Here is the final result.

The Sound of the Pi Sequence

Here are several pictures of the build.





We’re getting ready to start a BECMI/OSR campaign and so I decided to review the following BECMI/OSR products:

  • Rules Cyclopedia
  • Labyrinth Lords
  • Dark Dungeons
  • Blood & Treasure
  • Swords & Wizardry
  • Red & Blue Books with B/X Companion

What I discovered was that all roads point back to the Rules Cyclopedia. To me, it’s the best book that I use to look up all sorts of things. It’s not the be-all, end-all of sources, but it’s my go-to.

I have to admit that back in the 80’s when I was playing original BECMI/AD&D, our group jumped on the AD&D products immediately, and I never really played too much in the Mystara setting. It’s a shame because I now believe that Mystara is the best setting for playing the type of BECMI/OSR game we’re going to be playing.

Also, we’re going to be using Chapter 5 of the RC which means Weapon Proficiencies and General Skills will be used extensively. The Mystara section and Chapter 5 are two more reasons why the RC is the source of choice. The following document clarifies certain rules that will be used in the campaign:

Session Zero for Mystara Campaign Using Rules Cyclopedia and Labyrinth Lord

To me, the coolest part of what we’re going to be running is using a very specific set of character classes. My players can only choose from the following 16 classes. These classes come from James Spahn of Barrel Rider Games:






Bounty Hunter




Rune Smith



Sword Master

Undead Slayer


Wild Wizard

I took all of these classes and made a resource for the players to use.

Since we’ll be utilizing Weapon Proficiency and General Skills, I found a character sheet online that has an entire page dedicated to these mechanics. I’m not sure of its origin, but it’s perfect for our campaign.

D&D Character Record Sheet (Knotwork)

Finally, the one area of adventure that I just couldn’t find a system that I truly loved was the Hex Crawl. I’m sure there are numerous systems that are just fine, but I wanted to make travel and encounters have a simple system and use the groups’ skills.

I found the perfect set of encounter tables online. They were created by Jed McClure and he calls them Wilderness Hexplore. The system was designed for a map with absolutely no idea what lies beyond the home hex you start on. Since we’ll be in the Mystara campaign world, I modified his method, but I still think his tables are pretty robust.

Jed McClure_Wilderness_Hexplore_revised

My system utilizes his tables, but it requires the party of adventurers to be more involved in taking on certain roles as the group travels. Here is the revised system that utilizes skills from the General Skills list in the RC.

Overland Travel Rules for BECMI & OSR

One of the first games I ever created was a Gladiator game called The Colosseum. Don’t go buy it, though. It’s bad. I mean, the concept was good in many parts, but the combat was fairly dull. I’ve always intended to go back and re-develop the game, but it was always something on the back burner.

Lately I’ve been getting into the game Labyrinth Lord. It’s basically BECMI re-skinned and quite awesome!

I put together a campaign path that runs through a whole bunch of old core modules set in Mystara. The path (with options to change the path in branching directions looks like this:

  • B-2 Keep on the Borderlands (Lvl 1-3) or DDA1 Arena of Thyatis (Lvl 2-3)
  • X-1 Isle of Dread (Lvl 3-7) or DDA2 Legions of Thyatis (Lvl 3-4) if DDA1 was used and then run X-1.
  • X-13 Crown of Ancient Glory (Lvl 7-10) if players want to remain in Mystara, HWA1 Nightwail (Lvl 6-8) if players want to explore Hollow World.
  • HWA2 Nightrage (Lvl 7-9) if they chose HWA1
  • HWA3 Nightstorm (Lvl 8-10) if they chose HWA1 & 2
  • X-10 Red Arrow, Black Shield (Lvl 10-14) [all paths merge here]
  • CM-9 Legacy of Blood (Lvl 15-19)
  • CM-6 Where Chaos Reigns (Lvl 17-19)
  • M-5 Talons of Night (Lvl 20-25)
  • M-1 Into the Maelstrom (Lvl 25-30)
  • M-2 Vengeance of Alphaks (Lvl 28-32)


You’ll notice under the first bullet that DDA1 begins at 2nd Lvl. I began to think of how character could play first level as Gladiators and this led back to my old game.

Well, when I sat down to read over my old game, I remembered why I hated it and I decided to see what else was out there. One of the first hits I got was the game I’ll be using as the core system to run this game: Are You Not Entertained?!

The game is extremely easy to play and is perfect for running quick and fun Gladiator battles. Plus, it’s FREE!

I printed it in booklet form and then printed the stats for the types of Gladiators on card stock to make their sheets. There are eight types (including a bear and lion).

I found 2 packs of Permes paper minis that were Gladiator themed to make the Gladiator minis. Both packs together was about $4.

I chose to use blue and red dice to represent the colors of Attack and Defense like on the cards.

Hit Points can be tracked using 20-sided dice and since Magic uses nice, big ones for the same thing, I just used a bunch of those.

Finally, I happened to be browsing the hobby store and found the perfect arena by Paizo. It costs about $9.

We ran the game to test it out and two things I chose to adjust. One thing I found was that the battles tended to remain stationary. There’s no real incentive to move around once combat has started. So, in my supplement, I chose to add an incentive to move around more. The second thing I noticed was that combat damage can be hard to inflict. To adjust the option to make the battle move along even faster, I added some additional options to Advancements. I also wanted to be able to import this into a Savage Worlds Weird Wars Rome game, so I added four new types of Gladiator. You could consider this an advanced rules supplement:

Blood on the Gladius

You could very easily drop this into any RPG in various ways. It’s fun to just run it by itself and conduct numerous variations on tournaments and house rules.

Here is a handy Gladiator Tournament Brackets I created.

One final touch is your Gladiator name and background.

Here is a sample stable of Gladiators created from this and ready for fighting in an 8-man tournament. I used Thyatis instead of Rome, but you get the gist.


I had idea of how to use my nifty Chessex Goblin Dice for a non-rpg game for the whole family.

After the conference, I still had 5 dice, so I created Goblin Yahtzee!

Goblin Yahtzee



I’ve been toying around with a method to play Savage Worlds in a streamlined, solitaire style. The method I created requires the following products. The first is the Map & Dice deck from Inked Adventures. Each card includes a small geomorph dungeon section, suit and card number, and die results for a d6, d20, and d100. I created a Setting Rule that allows you to spend a Benny to use the dice results on the cards rather than the number you rolled. If, for example, the card had a 6 on a d6, you could spend a Benny a get an Aced die result!

I, once again, used Gold & Glory to create a random character. That is the character you must use for the 10 rounds of play. You’ll also need the Savage Worlds Deluxe Explorer’s Edition and the Fantasy Companion.

I chose to use the Fantasy Companion character sheet for the play tests.

You’ll need a standard set of Polyhedral dice as well as a Wild Die. A set of percentile dice and an additional d10 to help track rounds are handy.

The goal is not only to survive 10 rounds (you could make it longer, too, to see how long you survive!), but to also see how much treasure you can accumulate each time you play. I converted everything to gold pieces just to make it easier. Don’t forget to calculate the value of magic items should you find those as well. Also, monsters in the Fantasy Companion have a treasure rating; don’t forget to loot the monsters you defeat.

Basically, each suit of the cards represents a different type of encounter: Spades = Traps, Hearts = rest and healing, Diamonds = Treasure, and Clubs = a monster.

For my fights with monsters, I chose to use the Quick Combat and Quick Skirmish rules. Quick Combat is just one roll. Quick Skirmish can be several rounds, but is still just one roll. In other words, by using these rules, you never need to roll for the monsters.

Begin with 5 Bennies, shuffle the deck, and follow these guidelines:

SW Solitaire Dungeon

Not long ago I decided to order a couple of Call of Cthulhu RPG materials. I found a great copy of “Dreamlands: Roleplaying Beyond the Wall of Sleep”. This is such a great setting book for the Dreamlands!

In the introduction, Sandy Petersen and Chris Williams provide sources for where they gathered their material from. While the Lovecraft citations are, of course, required, they also mentions works by Brian Lumley, Clark Ashton Smith, and Gary Myers.

My pursuit of these lesser known books by Myers, Lumley, and Smith began.

This would be a comprehensive library of Dreamlands related material that could be referenced for any adventures you might want to run in the Dreamlands for your role playing.

The Myers book was a pleasant surprise. It is a small, hardback edition. It might even be the first edition of the book. Pendragon Fine Books of California had it for a very reasonable price.

As far as I know, the only published Savage Worlds setting that takes place in the Dreamlands is the crossover book done for Aching! Cthulhu and DUST, which is an epic adventure!

And I must once again mention the map that ties all of this together at the gaming table, the map by Jason Thompson:

Map of the Dreamlands

Thompson also mentions Gary Myers as well as Lord Dunsany.

So, I decided to create some fantasy characters using a combination of Sean Patrick Fannon’s new product called A Hero Will Rise: Epic Fantasy and the random fantasy character generator in Giuseppe Rotunda’s Gold & Glory: Seven Deadly Dungeons. This was a fun way to create some interesting characters with good backgrounds as well as bonds between each of the characters.

I also decided I liked the retro look and feel of Middle Kingdoms Adventure and Trading Company’s Basic Savage Worlds Fantasy Character Record Sheet.

The results needed to be fudged ever so slightly with the classes so I could get a diverse group of adventurers; but I really enjoy just sitting down and creating characters using these products! In addition, I think these products go nicely together and have an old school, early D&D feel.

The end result is a group comprising a Male Human Cleric, a Male Elf Fighter (kind of Rangerish), a Male Elf Rogue, and a Female Human Wizard.

Kaervold Stormcrow

Wylghin Arazord

Skyjard Arazord

Lira Daravik


I wanted to share the high resolution pic of the goblin stronghold I created for Saga of the Goblin Horde.

Vulgorath G&G

First of all, there’s Saga of the Goblin Horde, which is epic, fun, and hilarious! Then, there’s this nifty little system called Gold & Glory  that has a certain reminiscence of Old School D&D – we’re talking back in the late 70’s and early 80’s type of dungeon crawly feel. Add a little home brew notes from Rob Randolph’s running of Saga of the Goblin Horde, and I present my Goblin Stronghold with a Random Encounter Generator.

The complex can be used in many ways. Any time that the gang gets their mission from Chief Bignose, use the random encounter generator one or two draws to determine what antics the gang goes through leaving the caves. Simply draw three cards from a pool of cards 2-10 of all suits (remove aces and face cards). Dice will also be used as well. Interpret the cards per the suggestions in the Gold & Glory core book. You’ll also need to have a copy of Saga, the Savage Worlds Deluxe Explorer’s Edition, and the Fantasy Companion.

Another use is to generate betweener missions during the Plot Point Campaign in Saga. Or, you can simply use everything for your own ideas to execute little side missions within the caves.

I tried to keep everything as “theater-of-the-mind” style of play as possible. It’s up to you if you want to actually set out miniatures and set pieces, but it shouldn’t be necessary.

And here is the pdf of the tables:

Vulgorath G&G

Genghiscon 41 is just around the corner and this year, instead of just attending to play in the fantastic games, I’ve decided to run a couple of sessions of Richard Woolcock’s “Saga of the Goblin Horde”.

Genghiscon 41

I’ve been working diligently to prep for the sessions and wanted to go through some of the gaming aids and table props I’ve put together for the convention.

To begin with, there’s the setting book.

I used the files that Richard provided to order the hardback edition through Lulu. It was super easy and quick to upload the ready-made files. The final result looks amazing next to my other Savage Worlds books, too.

Saga of the Goblin Horde

I also wanted to create a convention-worthy map and turned to the files that Frank Turfler made just for SotGH.

Hex Terrain Tile Cave System

I printed the hexes on card stock and affixed them to a foam board.

The final result was perfect!

I also put in a session making homemade Bennies.

This was done by printing the pictures on labels and then cutting them to fit the center circle of some poker chips. I also ordered some dice that fit the theme, but I placed an order with Chessex to create special SotGH Wild Die.

I scrounged around on the internet looking for a deck of goblin cards. I didn’t find anything that specific, but I did find this amazing deck with artwork by Ian Schofield.

It can be found here.

Orcs and Undead Deck

The deck even has a companion smart phone app that is a solitaire game with the same artwork on the cards. Pretty cool!

I also stocked up on goblin miniatures from Reaper Miniatures. I love running games with miniatures and these are perfect for the setting.

Finally, I created a GM screen using the tri-fold version that Pinnacle sells.

All in all, the prep work has been fun in and of itself. Still, I can’t wait to run this setting at Genghiscon 41. Saga is a fun twist on the Fantasy genre of RPGs and I think it will be hilarious. I’ll be sure to get some good pics of the action!